Variable Annuities: the GMxB guarantees and the GMWB's optimal surrender behaviour

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Type de document Mémoires
Auteur(s) JIMENEZ M.
Date de référence 09/30/2009


Variable Annuities represent a major part of the present annuity market. Two main types of Variable Annuities guarantees can be distinguished: the guarantees in case of death (GMDB) and the guarantees in case of survival (GMAB, GMIB, GMWB and GLWB). In the French market the guarantee in case of death is known by the name of “garantie plancher” and is well developed. On the contrary, the guaranties in case of survival are less developed. In particular, the withdrawal guarantees (GMWB and GMLB) have just appeared in France. The present report presents different analytical approaches to value and hedge the Variable Annuities’ guarantees. A keen attention will be given to the GMWB guarantee. We will introduce a new valuation approach for GMWB inspired on previous approaches. We will profit from this approach to study the capital requirement related to this product. The report is composed of three parts:
• First, each GMxB guarantee will be described with some of its variants. The market of Variable Annuities will be introduced throughout some figures, followed by the analysis of this products market.
• Later, we will consider the GMDB, GMAB and GMIB guarantees. We will present some basic results for each of these guarantees, illustrated by numerical examples. We will not pursue to expose these guaranties in a profound manner.
• At last we will consider the case of no surrender, of optimal partial surrender and of optimal total surrender of GMWBs. We will also dedicate a Chapter to give some ideas on the valuation of the GLWBs.
In the total surrender GMWB Chapter we will present a new approach to the GMWB guarantees which is very adequate to this product. This approach will allow us to study the withdrawal behavior of the policyholders. It should be noted that GMWB products are particularly sensible to policyholder behavior. Once our main GMWB framework is presented we will profit from it to study the impact of interest rate, equity, mortality and longevity risk. In order to do so we will follow a QIS4 standard methodology approach. The results will provide us with a keen insight of this guarantee.

Mémoire complet

>Mémoire Martin JIMENEZ.pdf

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